text:
\section{Introduction}

    The old idea that the QCD running coupling ``freezes'' at low energies
has been phenomenologically successful in a wide variety of contexts.
(See Refs. \cite{mat,webber} and references therein.)  Theoretical
evidence that ``freezing'' does occur, and for purely perturbative reasons,
comes from the third-order calculation of $R_{e^+e^-}$ \cite{r2} which,
when ``optimized'' with respect to renormalization scheme, yields such
behaviour \cite{mat}.  Pad\'e approximant methods indicate a similar
conclusion \cite{eks}.  Another approach is the Banks-Zaks (BZ) expansion
\cite{bz,white,grun,st}, within which ``freezing'' is natural and
ubiquitous.  The relevance of the BZ expansion to low-energy QCD
phenomenology hinges on an extrapolation in the number of (massless) flavours,
$n_f$, from $16{\scriptstyle{\frac{1}{2}}}$ down to about 2.  Our point in this paper is that
the credibility of this extrapolation has been significantly enhanced
by the recent calculation of the QCD $\beta$ function to 4 loops \cite{rit}.

     The BZ expansion \cite{bz}-\cite{st} is an expansion in
$n_f^{\rm crit} - n_f$, where $n_f^{\rm crit}$ is the critical number
of flavours at which asymptotic freedom is lost; {\it i.e.}, where the first
$\beta$-function coefficient changes sign.  In QCD $n_f^{\rm crit}$ is
$16 {\scriptstyle{\frac{1}{2}}}$.  For $n_f$ slightly less than $16 {\scriptstyle{\frac{1}{2}}}$ the $\beta$
function starts out negative, but quickly turns positive, and there is
thus an infrared fixed point $a^*$ close to the origin \cite{cas,bz}.
Provided the couplant $a(\mu)$ initially lies between 0 and $a^*$
(necessary for asymptotic freedom), the couplant will ``freeze'' to
$a^*$ as the energy scale $\mu$ tends to zero.  Thus, in the BZ
expansion, ``freezing'' is natural and universal and will occur for all
$n_f < 16 {\scriptstyle{\frac{1}{2}}}$, unless or until the BZ expansion breaks down.

     Ref. \cite{st} has suggested that the BZ expansion is qualitatively
relevant to the real world where only 2 or 3 quark flavours are light
compared to the QCD $\Lambda$ scale.  The crucial issue is whether the
expansion shows reasonable numerical convergence when $n_f \approx 2$.
Assuming good behaviour, Ref \cite{st} made a prediction for a certain
coefficient.  As we discuss, this prediction is borne out by the recent
calculation of the QCD $\beta$ function to four-loops \cite{rit}.

     The plan of the paper is as follows:  Section 2 presents the notation
and extracts the relevant coefficients.  Sections 3 and 4 discuss the
BZ expansion for quantities at $Q = 0$ and at general $Q$, respectively.
An important role is played by $\gamma^{*}$, the slope of the $\beta$
function at the fixed point, and we discuss its coefficients (the
``universal invariants'' of Grunberg \cite{grun}) to fourth order.
Sect. 5 contains concluding remarks.  Appendix A summarizes the
results for a general $SU(N)$ colour group.  Appendix B discusses
the issue of renormalization-scheme (RS) invariance and the notion of
`regular' and `irregular' schemes.  The Higgs-decay case, which we argue
is not a good guide to infrared behaviour, is discussed in Appendix C.

\section{Notation}
     We write the $\beta$ function in the form:
\begin{equation}
\label{eq: beta}
\beta \left( a\right) \equiv \mu \frac{da}{d\mu} = -b a^2 \left( 1 + ca +
c_{2} a^2 + c_{3} a^3 +\ldots \right) \,,
\end{equation}
where  $a \equiv  \alpha_{s}/\pi$.  The coefficients, in the $\overline{\rm MS}$
scheme, are \cite{cas,c2,rit}:
\begin{eqnarray}
\beta_0 = 2b & \! \! = \! \!& 11 - \frac{2}{3} n_f \,,
\nonumber \\
\beta_1 = 8 bc & \! \! = \! \! & 102 - \frac{38}{3} n_f  \,,
\nonumber \\
\beta_2 = 32 b c_2 & \! \! = \! \! & \frac{2857}{2} -
\frac{5033}{18} n_f + \frac{325}{54} n_f^2 \,,
\\
\beta_3 = 128 b c_3 & \! = \! &
\left( \frac{149753}{6} + 3564 \zeta_3 \right)
- \left( \frac{1078361}{162} + \frac{6508}{27} \zeta_3 \right) n_f
\nonumber \\
& \!\!\!\!& \mbox{}
+ \left( \frac{50065}{162} + \frac{6472}{81} \zeta_3 \right) n_f^2
+ \frac{1093}{729} n_f^3.
\nonumber
\end{eqnarray}
Here $\zeta_s$ is the Riemann zeta-function ($\zeta_3 =1.202056903 \ldots$,
$\zeta_5 = 1.036927755 \ldots$).

    For $n_{f}$ just below $16 {\scriptstyle{\frac{1}{2}}}$, the $\beta$ function has a
zero at $a^{*} \sim -\frac{1}{c}$, and $a^*$ is asymptotically
proportional to $(16 {\scriptstyle{\frac{1}{2}}} - n_{f})$.  Its limiting form:
\begin{equation}
a_{0} \equiv \frac{8}{321}\left( 16 {\scriptstyle{\frac{1}{2}}} - n_{f}\right)
\end{equation}
serves as the expansion parameter for the BZ expansion \cite{st}.  Because
the constant of proportionality is so small, $a_0$ remains small ($\le 0.4$)
even with $n_f=0$.  To proceed, one re-writes all perturbative coefficients,
eliminating $n_f$ in favour of $a_0$.  The first two $\beta$-function
coefficients, which are RS invariant, become:
\begin{eqnarray}
b &=& \frac{107}{8} a_{0},  \\
c &=& -\frac{1}{a_{0}} + \frac{19}{4}.
\end{eqnarray}
Within the class of so-called `regular' schemes \cite{grun,st}, which
includes $\overline{\rm MS}$, perturbative coefficients have a polynomial dependence
on $n_f$, and we may write
\begin{equation}
\label{ciexp}
c_{i} = \frac{1}{a_{0}} \left( c_{i,-1} + c_{i,0} a_{0} + c_{i,1} a_{0}^2
+ \ldots \right).
\end{equation}
The coefficients, in $\overline{\rm MS}$, are collected in the table below.

\begin{center}
\begin{tabular}{|rclcr|}
\hline
$c_{1,0}$ &=& $\frac{19}{4}$ &=& 4.75 \\
\hline
$c_{2,-1}$ &$=$& $- \left( \frac{8}{107} \right)
\left( \frac{37117}{768} \right) $ &=& $-3.61$  \\
$c_{2,0}$ &=& $\frac{243}{32}$ &=& 7.59 \\
$c_{2,1}$ &=& $\left( \frac{107}{8} \right)
\left(  \frac{325}{192} \right) $ &=& 22.6 \\
\hline
$c_{3,-1}$  &=& $ \left( \frac{8}{107} \right)
\left( \frac{53981}{1152} + \frac{5335}{32}\zeta_3 \right) $
&=& 18.5 \\
$c_{3,0}$ &=& $-\frac{1544327}{13824} - \frac{16171}{288}\zeta_3$
&=& $-179$ \\
$c_{3,1}$  &=& $\left( \frac{107}{8} \right)
\left( \frac{2587}{96} +\frac{809}{144}\zeta_3 \right) $
&=& 451 \\
$c_{3,2}$ &=& $ - \left( \frac{107}{8} \right)^2
\left( \frac{1093}{3456} \right) $ &=& $-56.6$ \\
\hline
\end{tabular}
\end{center}

    The BZ expansion can be applied to any perturbatively calculable
physical quantity of the form:
\begin{equation}
\label{eq: R}
{\cal{R}}  = a \left( 1 + r_{1} a + r_{2} a^2 + r_{3} a^3
+ \ldots\right).
\end{equation}
In a `regular' scheme the coefficients $r_{i}$ are polynomials in $n_f$,
and hence in $a_{0}$:
\begin{equation}
\label{riexp}
r_i = r_{i,0} + r_{i,1} a_0 + r_{i,2} a_0^2 + \ldots .
\end{equation}
Note that a term $r_{i,j} a_0^p$ or $c_{i,j} a_0^p$ can be assigned a
degree $i+j-p$, and all terms in any formula must have matching degree.

    The prototypical example is the $e^+e^-$ ratio:
\begin{equation}
R_{e^{+} e^{-}}(Q) \equiv \frac{\sigma_{\rm tot} \left( e^{+} e^{-} \rightarrow
{\mbox{\rm hadrons}}\right)}{\sigma \left( e^{+} e^{-} \rightarrow \mu^{+}
\mu^{-}\right)},
\end{equation}
where, neglecting quark masses, we can write
$R_{e^{+} e^{-}} \left( Q \right) = 3
\Sigma q_{i}^2 \left( 1 + {\cal R}_{e^+e^-}\right)$, where ${\cal R}_{e^+e^-}$
has the form (\ref{eq: R}).  [Actually, for ${\cal R}_{e^+e^-}$ there is a
problem in that $r_2$ involves a term
$1.2395 (\Sigma q_{i})^2/(3 \Sigma {q_{i}}^2)$ whose $n_f$
dependence is ambiguous because it depends on the electric charges we
assign to the additional, ficticious quarks.  This arises because
$R_{e^+e^-}$ involves not just QCD, but its coupling to electromagnetism.
Fortunately, this term seems to make only a small numerical contribution.
We shall ignore it henceforth.]  The coefficients,
in $\overline{\rm MS}$ with the renormalization scale $\mu$ equated with $Q$, are
collected in the table below \cite{r2}:

\begin{center}
\begin{tabular}{|rclcr|}
\hline
  & & Coefficients in ${\cal R}_{e^+e^-}$.  [$\overline{\rm MS}$($\mu=Q$)] & & \\
\hline
$r_{1,0}$ &=& $\frac{1}{12}$ &=& 0.0833 \\
$r_{1,1}$ &=& $\left( \frac{107}{8} \right)
\left( \frac{11}{4} - 2 \zeta_3 \right) $ &=& 4.63 \\
\hline
$r_{2,0}$ &=& $-\frac{12521}{288} + 13 \zeta_3$ &=& $-27.85$ \\
$r_{2,1}$ &=& $ \left( \frac{107}{8} \right)
\left( \frac{401}{24} - \frac{53}{3}\zeta_3 + \frac{25}{3}\zeta_5 \right) $
&=& 55.0 \\
$r_{2,2}$ &=& $ \left( \frac{107}{8} \right)^2
\left( \frac{151}{18} - \frac{19}{3}\zeta_3 - \frac{\pi^2}{12} \right) $
&=& $-8.34$ \\
\hline
\end{tabular}
\end{center}

     Another example is the Bjorken sum rule:
\begin{equation}
\int_0^1 dx g_1^{\rm ep-en}(x,Q^2) = \frac{1}{3}
\left| \frac{g_A}{g_V} \right| \left( 1 - {\cal R}_{\rm Bj} \right).
\end{equation}
(The same QCD corrections, apart from a $(\Sigma q_{i})^2/(3 \Sigma {q_{i}}^2)$
term, appear in the Gross Llewellyn-Smith sum rule.)  The coefficients,
from Ref. \cite{bj} are listed below.

\begin{center}
\begin{tabular}{|rclcr|}
\hline
  & & Coefficients in ${\cal R}_{\rm Bj}$ [$\overline{\rm MS}$($\mu=Q$)] & & \\
\hline
$r_{1,0}$ &=& $- \frac{11}{12}$ &=& $-0.917$ \\
$r_{1,1}$ &=& $\frac{107}{8}$ &=& 13.38  \\
\hline
$r_{2,0}$ &=& $-\frac{1385}{72} - \frac{55}{4} \zeta_3$ &=& $-35.76$ \\
$r_{2,1}$ &=& $ \left( \frac{107}{8} \right)
\left( \frac{2749}{432} + \frac{61}{18} \zeta_3 - 5 \zeta_5 \right)$
&=& 70.25 \\
$r_{2,2}$ &=& $ \left( \frac{107}{8} \right)^2
\left( \frac{115}{72} \right) $ &=& 285.73 \\
\hline
\end{tabular}
\end{center}

     We mention that the same decomposition of coefficients is needed
in the ``large-$b$'' approximation \cite{max}, which employs the
opposite limit ($b \to \infty$, rather than $b = (107/8)a_0 \to 0$ as here).

\section{BZ Expansion: Q = 0}

     The fixed-point condition $\beta(a^{*}) = 0$ always has a solution
as a power series in $a_0$:
\begin{equation}
\label{astar}
a^{*} = a_{0} \left[ 1 + v_1 a_{0} + v_2 a_{0}^{2} +
v_3 a_{0}^{3} + \ldots \right].
\end{equation}
A straightforward calculation yields:
\begin{eqnarray}
\label{eq: AA}
v_1 &=& c_{1,0} +c_{2,-1},\nonumber \\
v_2 &=& (c_{1,0}+2c_{2,-1})(c_{1,0} +c_{2,-1})+c_{2,0}+c_{3,-1}, \\
v_3 &=&
c_{1,0}^3 + 6 c_{1,0}^2 c_{2,-1} +
c_{1,0}(3 c_{2,0} + 4 c_{3,-1} + 10 c_{2,-1}^2)
\nonumber \\
& & {\mbox{}} + c_{2,-1}(4 c_{2,0} + 5 c_{3,-1}) + 5 c_{2,-1}^3 + c_{2,1} +
c_{3,0} + c_{4,-1} \,. \nonumber
\end{eqnarray}
(Numerically, $v_1 =1.1366$, $v_2 =23.27$, $v_3 = c_{4,-1} - 138.6$,
in the $\overline{\rm MS}$ scheme.  The poor apparent convergence of the $a^*$
series need not bother us, since $a^*$ is RS dependent.)

     A physical quantity ${\cal R}$ will also have an infrared
limit given by a power series in $a_{0}$.  One simply takes the
perturbative expansion of ${\cal R}$, Eq. (\ref{eq: R}); substitutes
$a=a^*$, given by (\ref{eq: AA}); and re-expands in powers of $a_{0}$.
This yields:
\begin{equation}
\label{eq: RR}
{\cal R}^{*} = a_{0} \left[ 1 + w_1 a_{0} + w_2 a_{0}^{2} +
w_3 a_{0}^{3} + {\cal O}(a_{0}^{4}) \right],
\end{equation}
where
\begin{eqnarray}
w_1 &=& v_1 +r_{1,0},\nonumber \\
w_2 &=& v_2 + 2r_{1,0} v_1 + r_{2,0} + r_{1,1}, \\
w_3 &=& v_3 + (2 v_2 + v_1^2) r_{1,0} + v_1 (2r_{1,1} + 3 r_{2,0})
+ r_{2,1}+ r_{3,0}.\nonumber
\end{eqnarray}
These coefficients are RS-scheme independent (see Appendix B) and so their
numerical values are significant.  They should be order-1 numbers, if
all is to be well.

      For the $e^+e^-$ case, Ref. \cite{st} obtained the value of the
first coefficient, $w_1 = 1.22$, but $w_2$ could only be obtained as
$-18.25 + c_{3,-1}$, since $c_{3,1}$ was then unknown.  To quote
Ref. \cite{st}: ``For the expansion to be credible one needs
$c_{3,-1}(\overline{\rm MS})$ to be in the range, say, $+13$ to $+21$.''  This
prediction is confirmed by the new $\beta$-function result \cite{rit},
which yields $c_{3,-1} = 18.5$.  Therefore, $w_2$ is quite small,
$0.23$, giving a respectable series:
\begin{equation}
\label{ree}
{\cal R}_{e^+e^-}^* = a_0 \left[ 1 + 1.22 a_0 + 0.23 a_0^2 + \ldots \right].
\end{equation}
The next coefficient,
\begin{equation}
\label{wee}
w_3{\scriptstyle{(e^+e^-)}}
= c_{4,-1} + r_{3,0}{\scriptstyle{(e^+e^-)}} - 164.0,
\end{equation}
would require calculation of both $\beta$ and ${\cal R}_{e^+e^-}$ to one
more order.

      In the Bj-sum-rule case the corresponding result is
\begin{equation}
\label{rbj}
{\cal R}_{\rm Bj}^* = a_0 \left[ 1 + 0.22 a_0 - 1.21 a_0^2 + \ldots \right] ,
\end{equation}
where the coefficients are also of order unity.  It is interesting that
the ${\cal R}^*$ in this case is even smaller than in the $e^+e^-$ case.
The next coefficient is
\begin{equation}
\label{wbj}
w_3{\scriptstyle{({\rm Bj})}}
= c_{4,-1} + r_{3,0}{\scriptstyle{({\rm Bj})}}  - 203.7.
\end{equation}

\section{BZ Expansion: Nonzero Q}

    A formulation of the BZ expansion for quantities at a general $Q$
was derived in Ref. \cite{st}.  We briefly review the main ingredients.
First, we need a suitable form of the boundary condition for the
$\beta$-function equation.  Setting
$\hat{\beta} \left( x \right) \equiv \beta \left( x \right) / b$, we
write
\begin{equation}
\label{eq: int}
b \ln \left( \frac{\mu}{\tilde{\Lambda}} \right) = \lim_{ \delta \rightarrow
0} \left[ \int_{\delta}^{a} \frac{dx}{\hat{\beta} \left(x\right)} +
{\cal C}\left( \delta\right)\right].
\end{equation}
The constant of integration \({\cal C}\left( \delta\right)\) needs to be
suitably singular as $\delta \rightarrow 0$ and we choose \cite{opt,st}:
\begin{eqnarray}
{\cal C} \left( \delta \right) &=& \mbox{\rm P.V.} \int_{\delta}^{\infty}
\frac{dx}{x^2\left(1+cx\right)} \nonumber \\
&=& \frac{1}{\delta} + c\ln\delta + c \ln \left|c\right| +
{\cal O}\left(\delta\right).
\end{eqnarray}
Note that Cauchy's principal value (P.V.) is introduced to deal with the
pole at $x = -1/c$  when $c < 0$.  This choice amounts to a definition of
$\tilde{\Lambda}$, within a given RS.  [We use a tilde to distinguish it
from the older, but still widely used, definition of the $\Lambda$
parameter \cite{bbdm}.  The relation is $\ln(\Lambda/\tilde{\Lambda}) =
(c/b) \ln(2 \! \mid \! c \! \mid \! /b)$.  While the two definitions are not
dissimilar for small $n_f$, they become infinitely different as
$n_f \to 16 {\scriptstyle{\frac{1}{2}}}$.  In the BZ-expansion context the use of $\tilde{\Lambda}$
is much more convenient.]

    As explained in Ref. \cite{st}, it is convenient to put the $\beta$
function into the form
\begin{equation}
\label{betaf}
\frac{1}{\hat{\beta}\left(x\right)} = - \frac{1}{x^2} + \frac{c}{x} -
\frac{1}{ {\hat{\gamma}}^{*} \left(a^{*} - x\right)} +  H\left(x\right).
\end{equation}
where ${\hat{\gamma}}^{*}$ is $\gamma^{*}/b$, with $\gamma^{*}$ being
the slope of the $\beta$ function at the fixed point:
\begin{equation}
\label{gamstar}
\gamma^{*} \equiv \left. \frac{\beta\left(x\right)}{dx}\right|_{x=a^{*}}
= -b a^{*}
\left( 1 + 2 ca^{*} + 3 c_{2} {a^{*}}^{2}+ 4 c_{3} {a^{*}}^{3} +\ldots \right).
\end{equation}
As discussed below, $\hat{\gamma}^*$ can be obtained as a series in $a_0$.
The remainder function $H(x)$ can be expanded as a power series,
$H_0 + H_1 x + \ldots$, whose coefficients are of order $a_0$.

    One now inserts (\ref{betaf}) into (\ref{eq: int}) and performs the
integration.  One can then eliminate $a$ and $a^{*}$ in favour of
${\cal R}$ and ${\cal R}^{*}$.  In fact, since the result must be RS
invariant, one can --- without loss of generality --- short-cut this
step by utilizing the ``effective-charge'' RS in which $a \equiv {\cal R}$.
This leads to the formula
\cite{st}:
\begin{equation}
\label{eq: YY}
\rho_{1} = \frac{1}{\cal R} + \frac{1}{\hat{\gamma}^{*(n)}}
\ln\left(1- \frac{{\cal R}}{{\cal R}^{*(n)}} \right)
+ c\ln\left(\left|c\right| {\cal R} \right)
+ \sum_{i=0}^{n-4} \frac{H_i^{\rm (ec)} {\cal R}^{i+1}}{i+1}.
\end{equation}
The last term, involving the $H_i^{\rm (ec)}$ coefficients (of the
effective-charge scheme), is only relevant in fourth order and beyond.
Thus, for the first three orders the equation takes the same form, just with
the parameters $\hat{\gamma}^*$ and ${\cal R}^*$ approximated to the
appropriate order.  On the left-hand side, $\rho_1$ is the RS invariant
\cite{opt}
\begin{equation}
\label{eq: X}
\rho_{1} \equiv b\ln\left( \frac{\mu}{\tilde{\Lambda}}\right) - r_{1}
\equiv b \ln\left( \frac{Q}{\tilde{\Lambda}_{\rm eff}} \right),
\end{equation}
where $\tilde{\Lambda}_{\rm eff}$ is a characteristic scale specific to
the particular physical quantity ${\cal R}$.  It is related to the
$\tilde{\Lambda}$ parameter of some reference scheme (eg. $\overline{\rm MS}$) by
an exactly calculable factor $\exp(r_1/b)$ involving the $r_1$ coefficient
in that scheme, evaluated at $\mu=Q$.  (We caution that $\rho_1$ {\it cannot}
be split into ${\cal O}(1)$ and ${\cal O}(a_0)$ pieces in a RS-invariant
way \cite{st}.)

    Numerically inverting Eq. (\ref{eq: YY}) provides ${\cal R}$ as a
function of $Q$.  The resulting ${\cal R}(Q)$ naturally agrees with ordinary
perturbation theory to the corresponding order at large $Q$, but freezes
to the value ${\cal R}^{*(n)}$ as $Q \to 0$.  The BZ series expansion for
${\cal R}^{*}$ was discussed in the previous section.  The BZ expansion
for ${\hat{\gamma}}^*$ is obtained straightforwardly by substituting the
expansion of $a^*$ (Eqs. (\ref{astar}) and (\ref{eq: AA})) into
(\ref{gamstar}).  This gives:
\begin{equation}
{\hat{\gamma}}^{*} = a_{0}\left[ 1 + g_1 a_{0} +
g_2 {a_{0}}^{2} + g_3 {a_{0}}^{3} + \ldots \right]
\end{equation}
where,
\begin{eqnarray}
g_1 &=&  c_{1,0},\nonumber
\\
g_2 &=& {c_{1,0}}^{2} - {c_{2,-1}}^{2} -c_{3,-1}
, \\
g_3 &=&{c_{1,0}}^{3} - {4c_{2,-1}}^3
- 5 {c_{1,0}}{c_{2,-1}}^{2} - 4 {c_{1,0}} c_{3,-1}
\nonumber \\
& & \mbox{} - 2 c_{2,-1} c_{2,0} - 6 c_{2,-1} c_{3,-1} - c_{3,0} - 2c_{4,-1}.
\nonumber
\end{eqnarray}
It is noteworthy that certain terms of degree $n$ are absent in $g_n$:
$g_1$ does not contain $c_{2,-1}$; $g_2$ does not contain $c_{2,0}$ or
$c_{2,-1} c_{1,0}$; and $g_3$ does not contain $c_{2,1}$ or $c_{2,0} c_{1,0}$
or $c_{2,-1} {c_{1,0}}^2$.

      The significance of $\gamma^* = b \hat{\gamma}^*$ is that it
is the `critical exponent' governing how ${\cal R}$ approaches
${\cal R}^{*}$ as $Q \rightarrow 0$; asymptotically,
$ {\cal R} - {\cal R}^* \propto Q^{\gamma^{*}}$.
As pointed out by Grunberg, the $g_n$ coefficients are RS invariants,
and are universal, in the sense that they are not specific to some
particular physical quantity ${\cal R}$.  (See Appendix B for discussion
of some subtleties.)

      The new $\beta$-function result \cite{rit} enables us to determine
the numerical value of the second invariant; $g_2 =-8.99$.  (The exact
expression, for general $N$, is given in Appendix A.)  Hence the
${\hat{\gamma}}^*$ series is:
\begin{equation}
\label{gamser}
{\hat{\gamma}}^{*} = a_{0}\left[ 1 + 4.75 a_{0} - 8.99 {a_{0}}^{2}
+ \ldots \right]
\end{equation}
Clearly, the $\hat{\gamma}^*$ series is not as well behaved as the
${\cal R}^*$ series that we saw earlier.  In Fig. 1(a) we show $\gamma^*$
($= b \hat{\gamma}^*$) as a function of $n_f$.  (Fig. 1(b) shows
shows the same quantity normalized by $1/(ba_0)$.)  The lower and upper solid
curves are the first- and second-order results, respectively, while the
middle solid curve is the third-order result.  The dashed curve represents
the third-order result re-cast as a Pad\'e approximant:
\begin{equation}
\label{gampade}
\hat{\gamma}^* \approx  a_0 \frac{(1 + 6.64 a_0)}{(1 + 1.89 a_0)}.
\end{equation}
For comparison we also give, as the dotted curve, the prediction arising
from an optimized-perturbation-theory analysis of the $e^+e^-$ case
\cite{mat} (see comments in Appendix B).  The reasonable agreement between
the last three curves gives us some confidence that the extrapolation
to low $n_f$ is qualitatively valid, even if the quantitative precision is
not good.

      The next coefficient is
\begin{equation}
\label{g3}
g_3 = 269.44 - 2c_{4,-1}.
\end{equation}
We therefore predict that $c_{4,-1}(\overline{\rm MS})$ will turn out to
be somewhere around $135 \pm 10$.  Assuming that the $w_3$ coefficients
in (\ref{wee}) and (\ref{wbj}) are modest, we can expect that
$r_{3,0}{\scriptstyle{(e^+e^-)}} \approx 29 \pm 10$ and
$r_{3,0}{\scriptstyle{({\rm Bj})}} \approx 68 \pm 10$.

    Knowing $\hat{\gamma}^*$ and ${\cal R}^*$, we can numerically solve Eq.
(\ref{eq: YY}) to obtain ${\cal R}(Q)$ as a function of
$Q/\tilde{\Lambda}_{\rm eff}$.  The result, for the $e^+e^-$ case in
third order, is shown in Fig. 2 for $n_f = 14, 10, 6$ and $2$.
(It may be directly compared with similar figures for first and second
order in Ref. \cite{st}.)  Corresponding results in the Bjorken-sum-rule
case are shown in Fig. 3.  Note that the $\tilde{\Lambda}_{\rm eff}$'s
defining the units of $Q$ in Figs. 2 and 3 are not the same: however,
they are easily converted to a common $\tilde{\Lambda}$ using
Eq. (\ref{eq: X}).

\section{Concluding Remarks}

The result of van Ritbergen {\it et al.}'s \cite{rit} calculation of the
$\beta$ function to four-loops sheds much light on the BZ expansion.
It supports the idea that the expansion is relevant to the phenomenologically
interesting case of only two light quark flavors.  That, in turn,
implies perturbatively explicable ``freezing'' of the QCD running coupling
constant.

   We mention again the very interesting work on the ``large-$b$''
approximation (see \cite{max} and references therein) which draws on
large-$n_f$ results.  This is the opposite approximation to ours.
It extrapolates upwards from $n_f = - \infty$ ({\it minus}
infinity if the theory is to be asymptotically free) towards $n_f \approx 2$,
whereas we are extrapolating down from $n_f = 16{\scriptstyle{\frac{1}{2}}}$.  We think both
approximations are useful; neither is very precise, but both seem to be
qualitatively valid, and offer a great deal of insight into QCD.  Our
preliminary studies indicate that the large-$b$ approximation also
predicts ``freezing,'' and we hope to report on this shortly.

\vspace*{4mm}

{\bf Acknowledgements}:  We thank Ji\v{r}\'i Ch\'yla for correspondence,
particularly regarding the issues in Appendix B.
This work was supported in part by the U.S. Department of Energy under
Grant No. DE-FG05-92ER40717.

\newpage

\section*{Appendix A: SU($N$) generalization}

    The critical number of flavours is:
\begin{equation}
n_f^{\rm crit} = \frac{11}{2} N.
\end{equation}
The $\beta$-function coefficients in $\overline{\rm MS}$ are \cite{rit}
\begin{eqnarray}
\beta_0 = 2b & \! = \!&\frac{1}{3}(11 N - 2 n_f)
\nonumber \\
\beta_1 = 8 bc & \! = \! & \frac{1}{3 N}(34 N^3 - n_f (13 N^2 - 3))
\nonumber \\
\beta_2 = 32 b c_2^{\overline{\rm MS}} & \! = \! & \frac{1}{108 N^2} \left( 5714 N^5 +
n_f(-3418 N^4 + 561 N^2 + 27) + n_f^2(224 N^3 - 66 N) \right)
\nonumber \\
\beta_3 = 128 b c_3^{\overline{\rm MS}} & \! = \! & \frac{1}{1944 N^3}
\left( 601892 N^7 - 25920 N^5  + \zeta_3 (9504 N^7 + 684288 N^5)
\right.
\nonumber \\
& \!\! & \mbox{} + n_f \left[ - 485513 N^6 + 58583 N^4 - 21069 N^2 - 5589
\right.
\nonumber \\
& \!\! & \mbox{} + \left.
\zeta_3 (- 4320 N^6 - 118368 N^4 + 9504 N^2) \right]
\nonumber \\
& \!\! & \mbox{} + n_f^2  \left[ 69232 N^5 - 19816 N^3 -22428N
+ \zeta_3 (18144 N^5 - 13824 N^3 + 52704N ) \right]
\nonumber \\
& \!\! & \mbox{} + \left. n_f^3 [1040 N^4 - 616 N^2] \right)
\end{eqnarray}
The BZ expansion parameter becomes
\begin{equation}
a_0 = \frac{16}{3(25 N^2 -11)} (n_f^{\rm crit} - n_f)
\end{equation}
The invariant coefficients are
\begin{eqnarray}
b &\!=\!& \frac{(25 N^2-11)}{16} a_{0},  \\
c &=& -\frac{1}{a_{0}} + \frac{(13N^2-3)}{8 N}.
\end{eqnarray}
In $\overline{\rm MS}$
\begin{eqnarray}
c_{2,-1} &\! =\! & \frac{(-1402 N^4 + 242 N^2 + 33)}{48 N (25 N^2 - 11)},
\\
c_{2,0} &\! = \! & \frac{(318N^4 + 55 N^2 -9)}{384 N^2},
\\
c_{2,1} &\! = \! & \frac{(25 N^2 -11) (112 N^2 - 33)}{3072 N}
\\
c_{3,-1} &\! = \! & \frac{(14731 N^6 -30047N^4 - 58839 N^2 - 2277)}
{1152 N^2(25N^2 -11)}
\nonumber \\
& \! \! & \mbox{} +
\frac{11}{8}\frac{(25 N^4 - 18 N^2 + 77)}{(25N^2-11)} \zeta_3
\end{eqnarray}

    The Grunberg invariants, the coefficients in the expansion of
$\hat{\gamma}^*$ are:
\begin{eqnarray}
g_1 & \! \! = \! \! & \frac{(13N^2-3)}{8 N},
\\
g_2 & \! \! = \! \! &
\frac{(366782 N^8 - 865400 N^6  + 1599316 N^4  - 571516 N^2 -3993)}
{768 N^2  (25 N^2 - 11)^2}
\nonumber \\
& \!\!\!\! & \mbox{}
- \frac{11}{8} \frac{(25 N^4 - 18 N^2 + 77)}{(25 N^2 - 11)} \zeta_3.
\end{eqnarray}

\section*{Appendix B: Regular and Irregular Schemes}

     In this appendix we discuss renormalization-scheme invariance of
the BZ expansion results.  Since the expansion parameter
$a_{0} = \frac{8}{321} (16\frac{1}{2} - n_{f})$ is an RS-invariant pure
number, one expects the coefficients in the BZ expansion of a physical
quantity ${\cal R}$ to be RS-invariant, but it is important to have
confirmation.  We first consider the fixed point results at $Q=0$ (which
are independent of the $\tilde{\Lambda}$ parameter).

    In the text, as in Ref \cite{st}, we limited the discussion to
so-called `regular schemes' in which the coefficients in ${\cal R}$
and $\beta(a)$ have a polynomial dependence on $n_f$.  Such schemes
are natural in diagrammatic terms, since each fermion loop gives an
$n_f$ factor.  They are convenient for our purposes, since the
BZ-expansion coefficients are easily extracted from calculations
made in those schemes.  However, we emphasize that ``irregular'' schemes
are not necessarily ``bad.''  They will also lead to the same BZ-expansion
results, but the extraction of the BZ coefficients from calculations in those
schemes will be less straightforward.  An analogous situation arises,
for example, with gauge invariance; a certain class of gauges may
be convenient for some purposes, but inconvenient for others.

    It is easy to show the invariance of the BZ coefficients within the
class of `regular' schemes.  This was done in Ref. \cite{st} by
considering the RS-invariants $\rho_2, \rho_3, \ldots$ \cite{opt}
that are invariant combinations of ${\cal R}$ and $\beta(a)$ coefficients,
and expanding them in powers of $a_0$.  A `low-brow' version of the proof
is also instructive.  Consider a change of RS, $ a \mapsto a'$, where
\begin{equation}
\label{rstrans}
a' = a\left( 1 + u_{1} a + u_{2} a^{2} + \ldots \right).
\end{equation}
The coefficients in the expansion of ${\cal R}$ change to
\begin{eqnarray}
r'_{1} &=& r_{1} - u_{1}\, , \nonumber \\
r'_{2} &=& r_{2}- u_{2} -2 u_{1}r_{1} +2u_{1}^{2} \, ,
\end{eqnarray}
etc..  The $\beta$ function transforms to
$\beta'(a') =(\partial a'/\partial a) \beta(a)$, whose coefficients are:
\begin{eqnarray}
c' &=& c \nonumber \\
c'_2 &=& c_2 + u_2 -u_1^2 - u_1 c, \nonumber \\
c'_3 &=& c_3 + 2 u_3 + c u_1^2 - 2 c_2 u_1 - 6 u_1 u_2 + 4 u_1^3,
\end{eqnarray}
etc..  If both the primed and unprimed scheme are regular, then the
$c_i$, $c_i'$ and $r_i$, $r_i'$ coefficients are expandable as in
Eqs. (\ref{ciexp}), (\ref{riexp}), and the $u_i$ coefficients in the
scheme transformation can be expanded as:
\begin{eqnarray}
\label{uiexp}
u_{1} &=& u_{1,0} + u_{1,1}a_0 \, , \nonumber \\
u_{2} &=& u_{2,0} + u_{2,1}a_0 + u_{2,2}a_0^{2}\, ,
\end{eqnarray}
etc..  It is then straightforward to prove the invariance of the combinations
appearing in the BZ expansion of ${\cal R}$ and $\gamma^*$.  For instance,
from the relations
\begin{eqnarray}
r'_{1,0} &=& r_{1,0} - u_{1,0} \, , \nonumber \\
c'_{2,-1} &=& c_{2,-1} + u_{1,0} \, ,   \nonumber \\
c'_{3,-1} &=& c_{3,-1} - u_{1,0}^2 - 2 c_{2,-1} u_{1,0},
\end{eqnarray}
one sees that $r'_{1,0} + c'_{2,-1} = r_{1,0} + c_{2,-1}$,
and $c'_{3,-1} + (c'_{2,-1})^2 = c_{3,-1} + (c_{2,-1})^2$, showing that
these combinations are RS invariant.  Extending this procedure one can prove
the invariance of the higher-order $w_i$ and $g_i$ coefficients.

     Any scheme related to $\overline{\rm MS}(\mu=Q)$ by a transformation (\ref{rstrans})
with $u_i$'s expandable as in (\ref{uiexp}) is a `regular' scheme.
[It is noteworthy that in a general, regular scheme the coefficients
$c_{2,2}, c_{3,3}, \ldots$ are non-zero, while in a more restrictive class
of `strictly regular' schemes, of which $\overline{\rm MS}(\mu=Q)$ is an example,
these coefficients vanish.  This distinction is unimportant for the BZ
expansion, but matters for the large-$b$ approximation \cite{max}.]  The
`effective charge' (or `FAC') scheme, in which $a \equiv {\cal R}$ for
some specific physical quantity, is a `regular' (but not `strictly regular')
scheme.  However, it is easy to construct RS's that are `irregular' simply
by considering a transformation in which the $u_i$ depend on $n_f$ in a
non-polynomial fashion, so that the coefficients $r'_i$ are no longer
expandable in positive powers of $a_0$.  There is nothing intrinsically
`bad' about such schemes.  They can arise quite naturally.  For example,
the 't Hooft scheme, in which $c_2=c_3=\ldots=0$, is `irregular' \cite{max}.
[Recall that, in `regular' schemes, $c_{3,-1} + (c_{2,-1})^2$ is invariant
and does not vanish.]  The principle-of-minimal-sensitivity (PMS) scheme
for any given physical quantity is also `irregular.'  In both these
cases the $r_i$ coefficients have $1/a_0$ pieces.

    In a `regular' scheme, obtaining the BZ expansion to $n$th order requires
terms of order $n+1$ in the $\beta$ function, and of order $n$ in the
physical quantity ${\cal R}$.  In an `irregular' scheme the same information
is distributed among higher-order coefficients as well.  Starting from an
`irregular' scheme, one would require some knowledge of perturbative
coefficients to higher orders; maybe to all orders.  However, provided
one carefully kept all terms that could contribute to a given order in $a_0$,
one would obtain the same BZ expansion.

    Finally, we discuss the finite-$Q$ case.  Following Ref. \cite{st},
we have formulated the result as Eq. (\ref{eq: YY}), which is to be solved
numerically to obtain ${\cal R}$ as a function of $Q$.  This formula
involves the RS-invariant quantities $\rho_1$,, $\hat{\gamma}^*$,
${\cal R}^*$, $c$, and $H_i^{\rm (ec)}$.  The $\tilde{\Lambda}$ parameter
and $Q$ appear only in $\rho_1$.  The $H_i^{\rm (ec)}$ coefficients
(relevant only in 4th order and beyond) are directly related to the
$\tilde{\rho}_2, \tilde{\rho}_3, \ldots$ invariants of Ref. \cite{opt}
which can be conveniently redefined (hence the tilde) to coincide with the
$\beta$-function coefficients of the `effective charge' scheme \cite{exinv}.

    The RS invariance of the BZ expansion of $\hat{\gamma}^*$ \cite{grun}
is verifiable by the procedure discussed above.  It is expected because
of the well-known result \cite{gp} that the slope of the $\beta$ function
at a fixed point is an invariant.  However, there is an important
caveat to the last statement \cite{chyla}, which necessitates some
further discussion.  The quoted result follows by differentiating the
$\beta$-function transformation,
$\beta'(a') =(\partial a'/\partial a) \beta(a)$, to give
\begin{equation}
\frac{\partial \beta'}{\partial a'} =
\frac{\partial a}{\partial a'}
\frac{\partial^2 a'}{\partial a^2} \beta(a)
+ \frac{\partial \beta}{\partial a}.
\end{equation}
The first term vanishes at the fixed point --- provided that neither
$\partial a/\partial a'$ nor $\partial^2 a'/\partial a^2$
is singular there \cite{gp}.  Ch\'{y}la \cite{chyla} has pointed out that,
in general, it can be quite natural for those factors to be singular (and
arbitrary scheme transformation can of course make fixed points appear
and disappear!).  In general, then, the critical exponent $\gamma^*$ in
${\cal R} - {\cal R}^* \propto Q^{\gamma^{*}}$ as $Q \to 0$ is {\it not}
the same as $\partial \beta/\partial a|_{a=a^*}$.  However, these two
quantities will coincide in a large class of schemes.  It also seems
safe to assume that they coincide in the context of the BZ expansion,
where there is necessarily a fixed point at $a^* = a_0 + \ldots$.

    [We find that the 3rd-order PMS scheme, though `irregular,' also
yields $\gamma^* = \partial \beta/\partial a|_{a=a^*}$.  This requires
a detailed analysis of the optimization equations \cite{opt,mat} as
$Q \to 0$.  The PMS results (in the $e^+e^-$ case) for $\gamma^*$ are
shown as the dotted curve in Fig. 1.]

\section*{Appendix C: Higgs decay}

     In this appendix we discuss the case of Higgs-boson decay into
hadrons.  This seems to be a much more problematic than the cases
discussed earlier.  It could be viewed as conflicting with the
general picture we have presented.  We shall argue, though, that the
crucial role of quark masses in this quantity makes it unsuitable as
a guide to the infrared behaviour of perturbative QCD.  First, let
us discuss the numbers.

     The hadronic decay width of the Higgs has the form
$\Gamma_H = \frac{3G_F}{4\sqrt{2}\pi} M_H \sum_q m_q^2 \Gamma(a)$
with $\Gamma(a) = 1 + \Gamma_1 a + \ldots$, and where $m_q$ is the
running quark mass evaluated at some scale.  For $\Gamma_H$ there
is a factorization-scheme ambiguity (how much of the radiative
corrections should be absorbed into $m_q^2$, and much should be
left in the explicit series $\Gamma(a)$?).  However, one can define
the quantity \cite{ver}
\begin{equation}
{\cal R}_{\rm Higgs} = -\frac{1}{2} \frac{d \ln(\Gamma_H/M_H)}{d \ln M_H^2}
\end{equation}
which is free of this factorization-scheme ambiguity, and is a
physical quantity of the same form ${\cal R} = a(1+ r_1 a + \ldots )$
considered earlier.  The coefficients, from Ref. \cite{ver} are collected
in the table below.

\begin{center}
\begin{tabular}{|rclcr|}
\hline
  & & Coefficients in ${\cal R}_{\rm Higgs}$.  [$\overline{\rm MS}$($\mu=Q$)] & & \\
\hline
$r_{1,0}$ &=& $\frac{23}{12}$ &=& $1.917$ \\
$r_{1,1}$ &=& $\left( \frac{107}{8} \right) \left( \frac{11}{6} \right)
$ &=& $24.52$ \\
\hline
$r_{2,0}$ &=& $-\frac{503}{18} - \frac{55}{4} \zeta_3$ &=& $-44.47 $ \\
$r_{2,1}$ &=& $ \left( \frac{107}{8} \right)
\left( \frac{2935}{144} - \frac{7}{4}\zeta_3 - \frac{\pi^2}{3} \right) $
&=& $200.5$ \\
$r_{2,2}$ &=& $ \left( \frac{107}{8} \right)^2
\left( \frac{275}{72} - \zeta_3 - \frac{\pi^2}{12} \right) $
&=& $321.1$ \\
\hline
$r_{3,0}$ &=& $-\frac{22631621}{82944} - \frac{13939}{432} \zeta_3 +
\frac{4675}{48}\zeta_5 + \frac{107}{24}\pi^2 $ &=& $-166.6 $ \\
$r_{3,1}$ &=& $ \left( \frac{107}{8} \right)
\left(- \frac{208411}{3456} - \frac{20755}{288}\zeta_3 -\frac{355}{48}\zeta_5
- \frac{137}{192}\pi^2 \right) $ &=& $-2162$ \\
$r_{3,2}$ &=& $ \left( \frac{107}{8} \right)^2
\left( \frac{694303}{6912} - \frac{119}{4} \zeta_3 + \frac{25}{4}\zeta_5
- \frac{317}{96}\pi^2 \right) $
&=& $6901$ \\
$r_{3,3}$ &=& $ \left( \frac{107}{8} \right)^3
\left( \frac{985}{108} - \frac{5}{2} \zeta_3 - \frac{11}{24}\pi^2 \right) $
&=& $3808$ \\
\hline
\end{tabular}
\end{center}

      In Ref. \cite{h3} it was observed that, at third order in the
effective-charge (or `FAC') scheme, there is a fixed point with
${\cal R}^*_{\rm Higgs} \sim a^* \approx 0.15$.   The authors viewed this
as probably spurious.  Indeed, it is odd that it is only about half the
size of the frozen couplant found in the $e^+e^-$ case, and so is far
from the leading-order BZ expectation that $a^* \sim a_0$.  At 4th order
Ref. \cite{ver} finds that this fixed point is no longer present.
We have checked that the situation is much the same in optimized perturbation
theory \cite{opt,kss}.

      The $Q=0$ BZ series in this case is:
\begin{equation}
{\cal R}^*_{\rm Higgs} = a_0(1 + 3.05 a_0 + 7.67 a_0^2 + \ldots )
\end{equation}
whose coefficients are considerably larger than in the $e^+e^-$ or
Bjorken-sum-rule cases (Eqs. (\ref{ree}), (\ref{rbj})).  For a low number
of flavours the ``corrections'' are as big as the leading term, and
both the same sign.  (The next coefficient in the expansion is
$c_{4,-1}-109$ and is still unknown; our estimate (see Eq. (\ref{g3})
suggests that it is around $26 \pm 10$.)  One could conclude that this is
perhaps a case where the BZ expansion breaks down before $n_f=2$, so
that maybe there is no freezing in this case.

     We believe, however, the problem is that this quantity is just
not a useful indicator of massless QCD's infrared behaviour, because of
the way that quark masses are involved.  For exactly massless quarks
the hadronic Higgs-decay rate is zero, because the Higgs-quark coupling
is proportional to quark mass.  (The calculations neglect quark masses
in the radiative corrections but not, of course, in the overall coupling
factor.)  If we keep the quark masses finite when we consider, theoretically,
the limit $M_H \to 0$, we will trivially get zero as soon as the decay becomes
kinematically forbidden.  To avoid this we would need to consider a limit
in which $m_q$ tends to zero at least as fast as $M_H$; say
$m_q \propto (M_H)^{\kappa}$ with $\kappa \ge 1$.  But then
${\cal R}_{\rm Higgs}$ is not of the form $a(1 + r_1 a + \ldots )$, and
depends on $\kappa$, making it ill-defined.  These issues do not arise
for ${\cal R}_{e^+e^-}$ or ${\cal R}_{\rm Bj}$, which are meaningful for
massless quarks.

\newpage

redpajama_set_name: RedPajamaArXiv


Since JC's Funky Hair Ranch loves dogs so much they have added an addition to their pet family with the arrival of Wyatt Fitzpatrick, a.k.a. WyFi. He is a 17 week old Chaweenie who was found and on the side of the road and brought to PetsMart. Karla, the owner's wife, was at PetSmart and Wyatt leaped into Karla's arms and he is now a valuable member of JC's Funky Hair Ranch just like Nellie Roo.
From Mom and Pop stores, mid- level companies, to big box, many establishments are taking note that their customers want to bring along the family pet whether it's for a quick errand, eating or a long vacation. A growing number of corporations such as Google, Etsy, and Amazon allow their employees to bring their dogs to work, some corporations are so pet friendly that they have created dog parks and provide doggie treats at the reception desk.
According to recent studies the Millennials want their pets with them as they consider these animals as a big part of their lives. Pet ownership in the USA has tripled since the 1970s and today 68% of households own a pet. Millennials are known for their love of pets and for , and this includes seeking out pet friendly businesses. With such numbers, why would any business not allow pets? Those establishments, like JC Funky's Hair Ranch, that allow pets create very loyal customers.
Social Compassion in Legislation is an organization that sponsors and supports legislation that promotes the care, rights and protection of animals. While they are aware and are pleased with the growing trend of animals in the workplace they realize there is more to do. The organizations founder and President, Judie Mancusco helped draft a bill, Dining with Dogs, which recently passed both the Assembly and State Senate in New York City. "The bill allows restaurants that have outdoor areas to open them up to their patron's dogs if they so choose to. It does not mandate it; it makes it legal if the restaurant wants to. Regarding public health standards, the law allows specific guidelines for restaurants to follow to ensure health and safety codes. This legislation will help prevent life threatening situations for dogs since owners will no longer need to tie them up where they can be injured or stolen, or left in a hot car.
Moreover, studies have shown that having animals in the workplace can make workers more productive, while lowering stress levels. JC Mahan is the salon owner at JC's Funky Hair Ranch and has been a hair stylist for many years. JC loves pets, doing hair and making people happy and feel confident with their hairstyles. As a National Educator for Paul Mitchell Products for twenty years, he is a big believer in continuing education. JC is the only hair stylist in Oklahoma to receive the honor of being named a Master Associate by Paul Mitchell Education. JC's Funky Hair Ranch also works to educate each client on proper home hair care and styling techniques.
JC's Funky Hair Ranch it is not your regular salon. With its rustic wood paneled building that is filled with Cowboy-Funk decor; Funky Hair Ranch is an expression of JC's Feng Shui. JC's Funky Hair Ranch is best known for its amicability in their service and urge to teach about hair styling to their clients. Their large base of clientele just goes to prove their motto: Change is good. Change is my Friend. At JC's Funky Hair Ranch, we want you to feel special, provide quality hair services and let you lower your stress levels. So, come give your hair a treat, lower your blood pressure and relax with Nellie Roo and WyFi.


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Telsaan Tea has an open, versatile space with privately funded wi-fi for meetings and gatherings. Seating is available for up to 24 people. In general, small groups can meet here without reservations, unless extended business hours are needed.
Note: minimum rate charged is one hour with half hour increments thereafter.


Keywords Modeling, simulation and characterization of multi-junction solar cells.
2009 – Present | Institut National des Sciences Appliquées, Public Engineering School, Rennes, France.
Master's Degree in Materials Science and Nanotechnology engineering.
2011 - 2012 | Rochester Institute of Technology, Rochester, NY, USA.
Exchange program with INSA of Rennes in the Electrical and Microelectronic Engineering Department.
2009 | University Institute of Technology (IUT), Lannion, France.
Graduated with a two-year degree in Applied Physics specializing in Materials Science.
2012 – Present | SOITEC, Solar Energy BU, Bernin, France.
§ Extensive work to get a better understanding of the physical functioning of the devices with the focus on performance optimization.
§ Study and characterization of InGaP/InGaAs/Ge triple-junctions solar cells.
§ Setup and characterization of a new system measuring the spectral response of solar cells.
§ Spectral responsivity measurements of quantum dot solar cells.
§ Analysis and measurement of electrical properties of III-V semiconductor materials.
§ Optimization of metal contacts on GaN, InGaN films.
Project graduation consisting in the adaptation of a hybrid engine to a thermal miniature car.
Studied and characterized state-of-the-art triple junctions solar cells incorporing nanostructures such as quantum dots/wells.
Matlab; Labview; Silvaco; Quartus; Origin; PSpice; Comsol; CodeBlocks; VBA.


With the 2017-19 state budget now more than a month and a half overdue, increasing attention is being paid to the impact the delayed passage of the budget will have on schools, as evidenced by this Wisconsin State Journal article.
In a recent memo to members of the Legislature's budget-writing Joint Finance Committee (JFC), the Department of Public Instruction (DPI) has outlined the impact of the delay on various state school finance calculations for the 2017-18 school year, for public school districts, as well as private choice schools and independent charter schools.
One of the key dates is October 15, when the DPI is required by state law to certify state general school aid amounts for public school districts. School districts rely on these amounts and other data provided by the DPI in order to set their tax levies by the November 1 deadline.
The DPI indicates the 2017-19 biennial budget must be signed into law by October 3 to enable it to accurately run the October 15 General Aid Certification. The DPI plans to release these numbers to districts on Friday, October 13, because October 15 falls on a Sunday this year.
Although no specific changes are proposed in the budget to the state general school aid formula (i.e., no additional aid dollars are added) in the first year of the budget, the general aid calculation has grown increasingly complex in recent years as it now incorporates a number of aid deductions related to vouchers.
That calculation now includes a deduction from all school districts for the Independent Charter School Program, district-by-district aid deductions for statewide and Racine voucher programs and the special needs voucher program as well as a specific aid deduction to Milwaukee Public Schools (MPS) for the Milwaukee voucher program.
Because school districts have the authority to adjust their property tax levies to make up for these deductions, missing this deadline may result in insufficient state aid deductions, which the DPI indicates would increase costs to the state's general fund.
Another deadline identified by the DPI is October 27. In order for school districts to set their property tax levies with an adjusted revenue limit that accurately reflects their aid deductions for resident pupils who participate in the statewide or Racine voucher programs or receive special needs vouchers, the DPI indicates the budget must be signed into law by October 27. The DPI warns that failure to meet this deadline may result in districts under-levying the revenue limit adjustment allowed for aid deductions for choice and charter programs. Districts would not have the ability to be made whole for the aid deducted from their allotment once their levies have been set as this offset comes from increasing property taxes.
Under current law, per pupil payments for the various "choice" programs are indexed to the annual increase, if any, in the per pupil revenue limit adjustments and the increase in per pupil categorical aids provided to public school districts. In the absence of a signed budget bill, the DPI has no authority to increase the per pupil payment to schools in these programs above current law levels. Under the governor's original budget proposal, those per pupil payments were slated to increase by $217. It is uncertain what the actual increase will be because the budget hasn't been finalized and the status of some of the governor's proposed aid increases (e.g., Sparsity Aid–see separate blog post) is unclear.
The lack of finality regarding these per pupil payments to "choice" schools will affect the amount of aid deducted from public schools, which in turn will affect those public school district's ability to adjust their revenue limits and levies to compensate for these aid deductions and set their levies.
And, speaking of Sparsity Aid, the delay in passage of the budget likely means that the state's smallest and most rural school districts will not receive their Sparsity Aid payments on the same timeline as prior years. Historically, these aids have been paid in September, but the DPI memo indicates that with continued uncertainty about the amount of these payments and which districts will qualify to receive payments, these payments will likely be delayed and will not be paid out in September.
Finally, districts hoping to use the low-revenue ceiling adjustment could be out of luck if the budget isn't signed into law by October 27. Whether this adjustment will be provided to low revenue districts in the 2017-18 school year remains unclear. Assuming current proposals are approved by lawmakers and the governor, the DPI will need time to adjust revenue limit worksheets to enable these adjustments and time to double check district levies to make sure districts haven't exceeded their revenue limit authority if they use the low-revenue ceiling.


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However, my friend's mother had any issues with hers, which means you need to be cautioned. The grass isn't always greener on the side. Thus this situation could be closed at consumption because no true neglect is happening. In addition, the inside of my nose becomes dry.
Speaking of meetings, even if you possess a substance misuse problem, no matter your emotions about apps, now's the time to begin going. They might also have psychologists together with a huge choice of therapist for places they might be developmentally behind although A number of those children not only have social workers. In other instances, someone who becomes disabled can undergo rehabilitation to get ready for a fresh profession.
Society tells everyone they must be social, the only method would be to socialize in meaningful ways. You're worth it, you must deal with yourself. It's house of the country Pediatric Multiple Sclerosis Center.
It is not important how ridiculous or false a claim might be. Additionally, attempt to talk. Ms. Kikibruce, do not give them with the newspaper every time they do not say thank you.
Want at the very least a master's degree within this field. A social worker's task is one of the noble professions that we've got. These are only a few of many functions social workers play in society.
It is very important that our workers feel rewarded for their contribution and we're going to make certain that you've got access to all the training, development and training that you must accomplish your aims. Actions include things such as coordinating care recording keeping and helping in the increase of applications that are personalized, with different employees. They need to get comprehension and a knowledge of the policies in organizing services for clients included.
You are likely to get a network when you are bad. The very first step would be to have a rest. Before you try to apply for your prior job, possess a step back and reflect. This sort of work takes a whole lot of research and cooperation at various levels. Since they can function whatsoever even at their house also called their comfort zone, others simply don't have this option. They work within the field or within a facility.
Employee privacy is turning into an problem. Or you shot it as you fancied a shift. Disabled people these days are located in several jobs.
My very first assembly was gratifying. The worker is educated and indeed shocked he or she has trouble remembering the particulars of what was said for the remainder of the assembly. It's always valuable prior to opting to get a job interview, to prepare yourself.
Similar questions could be utilized to probe a assortment of distinct attributes. On occasion, you can want to alter fields. They may work in a range of specialties. A gym may be a good place to hone your abilities and gain knowledge that is invaluable . Use the opportunity.
Communicates with customer representatives, relatives, present and fresh customers and referral resources to guarantee the quality of solutions is supplied. The same considerations apply to some position at a health clinic. The great thing about a diem positions is you could earn a hourly wages that is higher than if you're a staff member that is regular.
Fill out forms to become certified as a supplier for this particular company. If your income is near the exterior choice, it can be scary to try to increase your income since you know you may quit getting aid, and at is higher than the increase in income. Even if you opt to babysit a larger volume of kids and want a license, it is less costly than opening a daycare enterprise.
A master's degree should raise the probabilities of acquiring a work much more. When you've got an opening you desire to be certain you employ the candidate for the job. Their group of distributors.
It involved in every facet of your life today even you opt not to utilize it. Just don't forget, stopping something which is wrong isn't a crime. They have to strive towards getting the entire life span of the customer back on course.
You may need to work a number of hours a month to keep your per diem standing. Solid organizational skills let you keep records and case files in purchase. You may receive a telephone call or you could get nothing.
Getting your lunch provides you spare time to socialize to your co-workers that are. The bodily needs of a massage career has to be factored in to any decision about the variety of hours you wish to get the business finished. Nevertheless speak with your boss if you are receiving poor hours.


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SportsVolleyball
Blue Raider Volleyball Steamrolls Alabama A&M
By Calvin White
Story by Phinehas Rollman/ Contributing Writer
MTSU volleyball welcomed the Alabama A&M Bulldogs to Alumni Memorial Gym on Wednesday night. The Blue Raiders were in control from start to finish, winning in three dominating sets as they gear up for the C-USA opener on Saturday.
"The team's mentality heading into the match was to keep playing our game and not play down, "said freshman phenom Adri Rhoda. I think we did a good job of that. I think we played our game."
Rhoda produced points all night for the Blue Raiders, leading the way with game highs in kills (9), and aces (5). However, Rhoda was not alone. MTSU had nine players with multiple kills and collected 15 aces throughout the match.
The Blue Raiders are now 11-3 on the season and have won eight out of their last nine matches, giving them the momentum they need heading into conference play.
"We're all really excited with the preseason we've had," Rhoda said. "We're starting the conference play against a really tough opponent but that's how we want it. We want to beat them and we're really excited. Our mentality is in the right place."
The tough opponent Rhoda is referring to is Western Kentucky, who will stroll into Murfreesboro boasting a 12-2 record as of Wednesday. Saturday's match begins at 2:00 p.m. in the Alumni Memorial Gym as the Blue Raiders seek to continue their hot start to the season into conference play.
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redpajama_set_name: RedPajamaCommonCrawl


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NewsOne Minute: Herman Cain Says Some People Shouldn't Vote
NewsOne Staff
Herman Cain: 'Stupid People Are Ruining America'
Cain pointed out that only 58% of registered voter actually voted in the last presidential election. "What about the 42% that stay at home?" he asked. He's not so sure they should be voting in the first place. "I have even heard people say, 'Well, I don't vote because I don't know what's going on,'" Cain remarked. "And I say 'good!' Stupid people are ruining America and I'm glad some of a them stay home." Read more.
Florida Extends 'Stand Your Ground' To Cover Warning Shots
Florida Governor Rick Scott signed into law Friday an extension of the state's controversial "Stand Your Ground" law, which would cover warning shots. According to Newsy, the bill was written with the case of Marissa Alexander in mind. Alexander, 33, was found guilty of aggravated assault and sentenced to 20 years in prison after firing what her defense claimed was a warning shot at the husband during a domestic dispute. An appellate court later overturned her conviction and ordered a retrial. Read more.
Florida Man Charged With Attempted Murder After Throwing Hot Grits
A Florida man is facing attempted murder charges after allegedly throwing a pan of hot grits and grease on a neighbor. Edward Holley, 60, was taken into custody Wednesday at an Orange County home after allegedly flinging the hot pan's contents on Darryl Blacknell, 29,MyNews13 reported. Blacknell, who had allegedly been sitting on Holley's porch, ran off screaming in pain while suffered second- and third-degree burns on 30% of his body. Read more.
Alabama Veteran Granted VA Benefits After More Than 50 Years of Denials
A Korean War Veteran's 56-year struggle for Veterans Affairs benefits is finally over. Willie McCall, 85, suffers from debilitating, combat-related health issues and was essentially forgotten by the federal government. Before totally giving up on his VA benefits, McCall's nephew, Freddie Porterfield, contacted NBC affiliate WSFA. McCall says during his time as a rifleman during the Korean conflict, the weather was so cold it left him with frostbite, jungle rot and circulation issues. He walks with a cane and has special orthotic shoes. Despite multiple diagnoses, he was denied VA benefits. His denials go back to the late 1950s. Read more.
NewsOne Minute: Herman Cain Says Some People Shouldn't Vote was originally published on newsone.com
GOP	, Herman Cain	, politics	, voting	, voting right
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FOUNDATION FOR END-OF-LIFE CARE INC
Transform dying into the final act of living well.
aka Hospice Foundation for End-Of-Life Care, Inc., Vitas Hospice Charitable Fund, Caring Foundations, LLC, | Hollywood, FL | www.foundationeolc.org
Mission & Vision Our goal is to provide compassionate assistance to hospice patients and their families on a nationwide basis by funding certain expenses that go beyond the hospice care benefit through our Special Needs Fund.
Dr. Richard B Fife
3440 Hollywood Blvd Suite 415
Hollywood, FL 33021 USA
Fundraising Contact
Patricia Lauck
Fundraising contact phone: (954) 272- Ext 9847
3440 Hollywood Blvd. Suite 415
Legal name of organization: Foundation for End of Life Care, Inc.
Hospice (P74)
Special Needs Program
The Foundation works nationally with social workers from a number of hospice programs and makes grants through its Special Needs Fund to assist patients and their families with extraordinary expenses that lie outside the realm of hospice care but are critically important to the patient's comfort or peace of mind.
The Foundation remains committed to working with hospice social workers nationally to help identify the patients and families they serve who lives have been changed not only by the health crisis they are facing but also by the financial crisis they face at the very same time by supporting them with financial grants to assist with everyday living expenses that are not met by the Medicare benefit.
To reach out to the public via social media efforts (web page, facebook, twitter) to align with like organizations to help educate the public at large about hospice and what it means, earlier access to hospice care, as well as the available resources to the patient population.
The Foundation For End-Of-Life Care is comprised of a well informed group of professionals who have made the hospice care sector their life's goal to bring about education, access, and quality care for those in need of hospice care. We are engaged in a broad stroke of social media outreach, engaging in local and national fundraising campaigns to also bring about awareness of hospice care.
The Foundation, since its inception has been helping families in financial crisis who are coping with the terminal illness of a loved one. More recenlty over the past six years the Foundation for End of Life Care, Inc., granted more than 6,000 special need grants for indigent patients and their families who are experiencing financial hardship. We provided essential items such as food, clothing, overdue rent and utility payments and last-minute travel for final reunions. Comfort items such as window air conditioners, pest control services and reading glasses also were funded for needy patients.
Hugh Westbrook
Foundation for End of Life Care, Inc.
Harold Wallace
Mary McKenna
Esther Colliflower
Foundation For End-Of-Life Care, Inc.
Richard Fife
Does the board conduct a formal orientation for new board members and require all board members to sign a written agreement regarding their roles, responsibilities, and expectations? Not applicable
Has the board conducted a formal, written assessment of the chief executive within the past year ? Not applicable
Have the board and senior staff reviewed the conflict-of-interest policy and completed and signed disclosure statements in the past year? Not applicable
Has the board conducted a formal, written self-assessment of its performance within the past three years? Not applicable
SOURCE: Self-reported; last updated 8/2/2021,
Financial trends metrics for five most recent years 2020, 2019, 2018, 2017, 2016*


You don't have to hibernate in winter—there are plenty of fun things to do in Detroit. Bundle up and get out there and enjoy Detroit!
Oh, and hockey. Looks like we'll have a (shortened) season after all.
1. Free Art Friday Detroit (Facebook link) - Every Friday local artists hide art around the city for lucky "scavengers" to find and keep. This week they go global with art from around the country and world. Follow their Facebook page and the #FAFDET hashtag on Twitter for clues. Go find art! January 11th.
2. Grown in Detroit - Head to the Detroit Historical Museum to see this documentary about the Catherine Ferguson Academy, one of only 3 schools in U.S. for pregnant and parenting teens. January 12—13.
3. Wild Winter Arctic Adventure - The Detroit Zoo is open year-round and is magical in the winter. Activities this weekend include ice carving demonstrations, arctic-themed arts and crafts, games and entertainment. January 12—13.
4. Metro Jazz Voices - The Sunday Music Bar at the DIA features this Detroit group perfoming selections of the Great American Songbook in four-part harmony. January 13th.
5. Charles H. Wright Museum of African American History - It's Charter One Free Family Second Sunday at the museum and admission is free. Special showings of the Voices of the Civil War film series & more. January 13th.


Sr Pritisha Brownley is a professional paediatric nurse who has worked in neonates, general paediatrics, haematology and oncology since 1990. Pritisha qualified in paediatrics and neonatal nursing science in 1996. She worked in Saudi Arabia in 1999 in paediatric oncology/haematology and completed oncology paediatric nursing whilst there. She has been working at CMJAH since 2010.
sponsored by the Carnegie Wits Diaspora Foundation.
Dr Capra is a paediatric oncologist who trained as a subspecialist in the UK & Canada and now works in Dublin. He is a keen cyclist and a member of various international clinical trial and research collaborative groups.
Dr Jennifer Geel is the chair of the Wits Paediatric Fund and Ministerial Advisory Committee on Cancer Control and Prevention. She is enrolled for a PhD, studying the relationship between simple blood tests and changes on PET-CT of children with Hodgkin lymphoma, hoping that more cost-effective versions of precision medicine may be possible in low and middle-income countries.
Dr Kenny Govendrageloo is a private practice Paediatric Cardiologist based at Sunninghill Hospital, Johannesburg. His interests are in the area of Diagnostic echocardiography, Foetal echocardiography, Cardiac intensive care, Pulmonary Hypertension, Lysosomal Storage Disease and a keen special interest Pompe Disease.
Jillian co-ordinates volunteer activities in the paediatric oncology unit at Charlotte Maxeke Johannesburg Academic Hospital, assisting with all non-medical activities. She also coordinates the Charlotte Maxeke Johannesburg Academic Hospital volunteer programme including selection, training, support and education of all the volunteers who give up their time to support the parents and children on an in- an outpatient basis.
Vanessa Hemp is a Clinical Psychologist who trained at Wits University. She was involved in forming The Day Clinic, a registered mental health clinic providing psychological services to adolescents and adults, where she currently serves as a director of adolescent services.
The only bone marrow registry in Africa with World Marrow Donor Association (WMDA) Qualification status. Bone marrow and stem cell transplants are used to cure children with various aggressive cancers, as well as rare and life-threatening diseases such as IPEX syndrome and inherited metabolic disorders. Based in Cape Town, the registry actively recruits and assists volunteer donors, as well as fundraising to perform international donor searches and transplants.
Chantel Lowry qualified as a social worker and started her career at Life New Kensington Clinic working with brain and spinal injury patients. However, she's always had a passion for children and so jumped at the opportunity to work in the paediatric oncology unit at Wits Donald Gordon Medical Centre. She is currently completing her Masters' degree, focusing on the influence of cultural practices on primary caregivers' coping ability and resilience when their child is diagnosed with cancer.
Dr Macaulay holds a Masters' degree in Genetic Counselling and a PhD in Clinical Epidemiology, both obtained from the University of the Witwatersrand (Wits). She is the Genetic Counselling Manager at the National Health Laboratory Service in Johannesburg, and a lecturer in the Division of Human Genetics at Wits.
Sr Pat McCusker is a paediatric nurse who has worked with children for more than 38 years. She has spent most of her time as a nurse working in the haematology/oncology unit. She loves the challenge of helping patients and the families of children with life-threatening illnesses and how to cope with treatment and associated problems. Pat is passionate about educating patients, families and nurses.
Dr Ramdin works as a senior Neonatologist, specializing in care and neurodevelopment of premature infants and sick neonates, at Charlotte Maxeke Johannesburg Academic Hospital, one of Southern Africa's largest tertiary and academic hospitals, and is the coordinator of the National Neonatal Resuscitation program and has recently embarked on a joint neonatal resuscitation program with Zimbabwe.


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Home Blogging Google to 'phase out' third-party cookies in Chrome, but not for two...
Google to 'phase out' third-party cookies in Chrome, but not for two years
Lawrence Sonoiya
Google will join Safari and Firefox in blocking third-party cookies in its Chrome web browser. However, unlike those browsers (which have already started blocking them by default), Google intends to take a phased approach. Justin Schuh, the director at engineering for Chrome, writes that Google's "intention is to do this within two years."
In those cookies' place, Google is hoping that it can institute a new set of technical solutions for various things that cookies are currently used for. To that end, it has proposed a bunch of new technologies (as have other browser makers) that may be less invasive and annoying than tracking cookies have become.
These new technologies are supposed to make it easier for advertisers to target certain demographics without laser-sighting down to specific people, ensure that the infrastructure many sites use for logins don't break, and help provide some level of anonymous tracking so advertisers can know if their ads actually converted into sales.
If it all came to pass, it would radically shift the way ad tracking and privacy work on the web. It could also open up entirely new vectors of tracking we have yet to imagine.
The rhetoric between browser makers is getting sharper
The context for Google's cookie-killing proposal is that there's a pitched battle being waged between browser makers to remake the future of privacy on the web. On the one hand are browsers like Safari and Firefox, browsers with code that increasingly take an absolutist stance against cross-site tracking. On the other is Google and Chrome, whose developers are trying to cut down on tracking without kneecapping revenue for websites.
The difference between them all isn't just whether and how to implement that tech, but when. Google wants to wait a bit, Apple and Firefox believe the crisis is already too big and have already started blocking third-party cookies — perhaps before there's a viable replacement for some use cases (and in some cases, they may not want there to be one).
The battle is big and the rhetoric is getting sharp. People accuse Apple of wanting to smother the web in favor of a walled-garden App Store. Others accuse Google of wanting to maintain an ad-tracking dystopia. Google worries that cutting off cookies now will encourage bad actors to switch to harder-to-stop fingerprinting methods, but then everybody notices that it's awfully convenient that Google doesn't want to stop ad tracking until later.
But because these are web people, the fights are happening in places you're probably not really watching: email lists, github, and W3C panels and working groups. Compared to other tech fights, it probably looks relatively tame and — like all standards bodies — moves quite slowly. But the stakes are sky high: a huge proportion of the ads you see on the web are driven by third-party cookies and part of an infrastructure that tracks and trades on your data and even your identity.
The technical replacements for cookies are complex, political, and not finished yet
The specifics of the proposals get very complicated very quickly, unfortunately, and make explaining third-party cookies seem elementary by comparison. At a high level, Google wants to create a "privacy sandbox," where websites are able to gather some information but ultimately hit a wall where the browser cuts them off. Apple has proposed an API for helping retail websites track conversions that Google seems to like, but the two companies don't agree on how much information should be allowed. There are proposals for grouping people into large demographic "flocks" and replacement mechanisms for logging in with third-party services.
These ideas and more are getting hashed out — and hopefully they will be, because failing to do so will mean a further fracturing of how different people experience the web. There's unlikely to be anything like 100 percent agreement, but the hope is that we'll get some kind of consensus on what should replace third-party cookies.
Those cookies were never really meant to do as much work — or contain and share as much information — as they currently do. The list of things that third-party cookies do is very long and finding agreement on how (or whether!) to replace them is going to take a long time.
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Il Governo Forlani è stato il trentottesimo esecutivo della Repubblica Italiana, il terzo dell'VIII legislatura.

Il governo rimase in carica dal 18 ottobre 1980 al 28 giugno 1981 per un totale di 253 giorni, ovvero 8 mesi e 10 giorni.

Il governo Forlani ottiene la fiducia della Camera sabato 25 ottobre 1980 con 362 voti favorevoli (DC, PSI, PSDI, PRI, SVP, Union Valdotaine), 250 contrari (PCI, PR, PDUP, Indipendenti di Sinistra, MSI), 9 astenuti (PLI). I votanti erano 612, i presenti erano 621. La rappresentante dell'Associazione per Trieste non partecipa al voto.

Il governo ottiene la fiducia del Senato mercoledì 29 ottobre con 188 voti favorevoli (DC, PSI, PSDI, PRI, SVP, Union Valdotaine) e 120 contrari (PCI, PR, Indipendenti di Sinistra, MSI). Poiché al Senato l'astensione valeva come voto contrario, i due senatori del PLI Malagodi e Fassino non partecipano al voto.

Cadde a seguito dello scandalo della loggia P2. Forlani si dimise il 26 maggio 1981.

Compagine di governo

Sostegno parlamentare

Appartenenza politica
 Democrazia Cristiana (DC): Presidente del Consiglio, 13 ministri, 28 sottosegretari
 Partito Socialista Italiano (PSI): 7 ministri, 17 sottosegretari
 Partito Socialista Democratico Italiano (PSDI): 3 ministri, 5 sottosegretari
 Partito Repubblicano Italiano (PRI): 3 ministri, 4 sottosegretari

Provenienza geografica
La provenienza geografica dei membri del Consiglio dei Ministri si può così riassumere:

Composizione del governo

Note

Voci correlate
Governi italiani per durata
Presidente del Consiglio dei ministri della Repubblica Italiana
Presidenti del Consiglio dei ministri della Repubblica Italiana

Altri progetti

Collegamenti esterni

redpajama_set_name: RedPajamaWikipedia


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Clean Transportation
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Crowdfunding Solar Projects for Non-Profits Now a Reality with Interest
by Walter Wang January 17, 2014 1 comment
Did you ever wonder why more non-profit institutions have not taken the plunge into solar energy? The short answer is that as non-profit institutions, such institutions are not able to utilize the tax incentives and other tax related benefits that often drive adoption of solar on a commercial scale in the US.
A new, sophisticated model for helping non-profits go solar has been developed by San Diego based CollectiveSun that utilizes a crowdfunding model to fund projects that provides a return on investment to investors over a 10 year period.
The first project that CollectiveSun completed was for the TERI Marshall House located in Vista, California. TERI Inc.'s mission is to change the way the world views and helps individuals touched by autism and special needs. The goal of the non-profit is to improve the quality of life for children and adults with developmental and learning disabilities.
Through the CollectiveSun crowdfunding campaign, $44,577.32 was raised from 27 investors. The lowest investment amount was $25 and the highest investment amount was $10,000. While every project will be different, this project is now paying 8% interest to the investors.
CollectiveSun partnered with Baker Electric Solar to design and install an 11.5 kW solar power system. The system will displace approximately 95 percent of the residence's electrical usage. How much will the installation of the system save TERI? It is estimated to save $77,228 over the 25 year life of the system.
The crowdfunding platform that CollectiveSun has developed moves impact investing into a new era. The impact is two-fold. Increasing adoption of solar energy and helping out a worthy cause.
Walter Wang is an energy tax policy expert and managing editor of CleanTechies. A list of his publications can be found here. Follow Walter on Twitter: @energytaxprof
CollectiveSuncrowdfundingnon-profitsolar energytax incentives
Walter Wang
Walter's contributions to CleanTechies over the past 4 years have been instrumental in growing the publications social media channels via his ongoing editorial and data driven strategies. He is the founder and managing director of Sunflower Tax, a renewable energy tax and finance consultancy based in San Diego, California. Active in the San Diego clean technology community, participating in events sponsored by CleanTech San Diego, EcoTopics, and Cleantech Open San Diego, Walter has also been a presenter at numerous California Center for Sustainability (CCSE) programs. He currently serves as an adjunct professor at the University of San Diego School of Law where he teaches a course on energy taxation and policy.
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Pharma production is 'too conservative' and needs to 'be bolder' in adopting nascent technologies, or be left behind by new models, suggested one MD.
Last week, panellists at Pharma Integrates assessed how significant an impact developing technology could make to standard manufacturing processes in the pharma industry.
Artificial Intelligence, digitisation, automation, 3D printing, and continuous manufacturing were reviewed during the 'Applying new technologies to the pharma value chain' panel discussion, which considered the validity of various approaches and urgency of adoption.
For each new technology, one quote has been selected to offer the panel's perspective on what the industry could see in the years to come.
3D printing is another technology wherein the potential applications have been discussed across a range of industries, and the US Food and Drug Administration has been particularly supportive of those companies looking to invest in the area.
One of the benefits of 3D printing in smaller batches is that tablets can be tailored to an individual patient's needs. During the discussion, Brian Henry, VP of drug product design at Pfizer, was more sceptical about its promise and posed the question of what new capabilities it brings to the table.
The potential for AI to revolutionise healthcare is often talked about, but Nick Lynch, CTO of Pistoia Alliance, said that curbing expectations of the technology will be crucial for practical implementations.
The digital revolution sweeping other industries is also having an impact on the pharma manufacturing sector. Mike Houghton, managing director of process industry and drives at Siemens, was strident in his views that pharma needs to adopt digital processes seen in other industries, and quickly.
No discussion on the future of manufacturing would be complete without continuous manufacturing. At the same conference, there was an in-depth discussion about what can be expected from this technology, but Henry referred to the technology as a "here and now" method – no longer to be talked of as the 'future' of manufacture.
On the topic of automation, Houghton again brought experience from other industries to point out how the pharma industry could be working harder to keep pace with innovation.


You may have a strong, well-developed company mission, and a vision that summarizes your organization's long-term plans and values. You may also have a brilliant content-marketing strategy, capable of attracting thousands of new people to your brand and keeping your current customers engaged. But, how well do these two areas of your brand strategy mesh?
My experience in working with small- to mid-sized businesses is that content-marketing strategies often get treated as separate entities, distinct from a brand's core mission and objectives. Why? Because content marketing is seen as an external platform, an advertisement, when it should be seen as both an external display and a showcase of your company's internal values.
In fact, you should be using your content-marketing strategy as a platform to support your brand's mission and vision. Here's how.
1. Recognize the importance of brand consistency.
Your first step should be to recognize the importance of brand consistency across all your platforms. This is the only way to build continuity with your customers.
Even if you have a personal brand, or display a logo in order to visibly demonstrate that this content was written by your brand, the content isn't "you" if it deviates from your main identity.
This is true no matter what medium you pursue, including social media marketing and paid advertising. Whenever a reader encounters your brand, he or she should have the same "feel," the same overall experience, which ties directly into the identity you created through your mission and objectives.
2. Draw topics from your mission and objectives.
Mimicking the aesthetics and style customers associate with your overall brand is a good way to tie your identity closer to your content campaign. But don't be afraid to draw new topics as well directly from your mission and objectives, to further your association with those causes.
For example, if you've explicitly stated your desire to reduce carbon emissions through the use of green technology, why not write the occasional post on how to be more environmentally friendly in the business world? If you're out to improve educational resources, why not highlight an interesting case study or news development in the educational realm?
3. Keep tone and demographics in mind.
It's also important to keep your demographics and your tone in mind throughout your content campaign: Let your mission and objectives dictate your operations along those line.
For example, say your mission is to help teams improve communication and bond with one another. Why not practice what you preach by writing in a more conversational, collaborative style, with ample opportunities for your readers to engage directly with you? This is a way of demonstrating your mission through your writing style, targeting exactly the types of people you sought to impress in the first place.
If your company's mission or objectives relate to corporate social responsibility, you'll probably be involved in efforts related to those objectives. For example, if you're all about building the economy in your local community, you might be a speaker at an entrepreneurial summit, or your team might volunteer for reconstruction efforts in your area to encourage more business development.
When you engage in these opportunities, show them off. Write a press release, or at the very least develop an on-site post covering your efforts. It makes a big impact when you put your money where your mouth is, so to speak.
5. Use images and video.
Throughout your content campaign, you should use images and videos to demonstrate your capacity to follow through on your mission and objectives. This can be applied to almost any of the strategies listed above; for example, you can include photos of your team participating in your cleanup efforts, or live-stream your speech at the entrepreneurial event.
Visuals make contentmore engaging, which leads to higher rates of social visibility and sharing, ultimately producing a more substantial boost for your brand.
6. Evaluate your touchpoints and customer reaction.
Throughout your efforts to incorporate more of your mission and vision into your content campaign, carefully evaluate your impact, just as you would any adjustment. Post new mission-related materials only periodically, never neglecting your core content campaign. And be sure to watch how prospective and current customers react. You'll almost certainly need to make adjustments along the way.
If your organization has a strong mission and vision at the center of its operations, there's no reason why your content-marketing strategy shouldn't be there to promote it and back it up. Let your customers know exactly what kind of company is behind the content they're reading, and make your values known to your readership.
As you've seen, all it takes is a handful of adjustments, including a few new types of content and modifications to your current lineup: The benefits can be highly significant to your brand visibility and reputation.


Wohler will boast the only platform-based closed captioning system capable of supporting all global standards.
Wohler Technologies is acquiring Europa Australia Pty Ltd, a closed captioning and data insertion company led by industry pioneer Elio Deluca.
Upon completion of the deal, Wohler will boast the only platform-based closed captioning system capable of supporting all global standards.
"Europa Australia is known for its ability to provide cost-effective solutions customized to the specific needs of each broadcast client," said Carl Dempsey, Wohler president and CEO. "The purchase of Europa Australia positions Wohler as a premier provider of closed-captioning and data control solutions. Through our new relationship with Elio and the Europa Australia engineering team, we will be equipped to respond to the development of closed-captioning standards in any country. This is a fantastic add-on to our existing talented engineering team. It is our ambition to be an extension of our clients' engineering resources and we can only do this is if we invest in the right talent and technology."
Europa Australia was established in 1996. Its closed-captioning processing technology developed by Europa Australia is compliant with CEA-608/708, the U.S. closed-captioning standard, and with OP:47, the Australian closed-captioning standard.
The Europa Australia technology is also available to other manufacturers who need to incorporate closed-captioning and extended data service solutions into their systems.
Australian broadcaster, Nine Network, has installed AmberFin iCR systems for video file transcoding and audio and caption processing at its new National Playout Centre (NPC) in Sydney. Nine Network's NPC is a highly efficient, file-based, HD broadcast facility. It simplifies operations by centralizing all playout for Channel Nine's 18 channels across Australia using a single HD file format.
RadiantGrid Intelligent Media Transformation Platform(TM)The Wohler RadiantGrid Intelligent Media Transformation Platform(TM) provides a consolidated, seamless software architecture that combines intensive media processing capabilities, such as transcoding, standards conversion, audio processing, caption processing, and quality control, with highly intelligent content management fabric and workflow orchestration layers. Based on an extensible service-oriented architecture, the platform integrates smoothly with editorial, archive, traffic, business process, and rights management systems.


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This delicate, fragrant wine was made from organically grown grapes, harvested by hand on gently rolling, sunny hills in Abruzzo.
Pale straw yellow in colour with greenish tinges. Since it is not filtered, it might have some slight veiling. The fragrance is fruity, with subtle floral and mineral notes, while the flavour is medium-bodied, delicate and savoury with an almondy finish. Excellent as an aperitif and with all seafood dishes, white meats and fresh cheeses.


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text:
Q: Crystal Report Datasource remap I am working with Crystal Reports and MS SQL Server.
I need to remap the crystal report to point to a different database on the same SQL Server. Is there an automated way of doing this, or do I have to remap for every single report? I am currently doing this by adding a new data connection, and then updating the stored procedure with the specified paramether to change database(catalog). Also, after remaping, the .asp that displays the report crashes like this:
Active Server Pages, ASP 0115 (0x80004005)
A trappable error (E06D7363) occurred in an external object. The script cannot continue running.
The code is:
Set mainReportTableCollection = Session("oRpt").Database.Tables
For Each mnTable in mainReportTableCollection
  With mnTable.ConnectionProperties
   .Item("user ID") = "<some_login_name>"
   .Item("Password") = "<some_password>"
   .Item("DSN") = "<some_DSN>"
   .Item("Database") ="<some_Database>"
  End With
Next

It runs, however, if i comment out the last two assignations.
Thanks in advance.
Yours trully, Silviu.

A: You'll find hereafter the procedure I use (I simplified it on the fly, suppressing our own objects and global variables). This procedure allows to redirect a report from an original connection used at development time to the active SQL server. It is written in VB and uses 2 main objects:

*

*The original report object opened through an instance of crystal report

*An ADODB connection being the active connection (called P_currentConnection) to the current SQL server

This function (could be also a sub) is called before viewing/printing the report object in the application. It can be used when distributing reports among replicated databases where users, depending on their location, connect to different servers/databases.
Public Function connectReportToDatabase( _
    P_report As CRAXDRT.Report)

Dim table As CRAXDRT.DatabaseTable, _

For Each table In P_report.Database.tables

    If table.DllName <> "crdb_ado.dll" Then
        table.DllName = "crdb_ado.dll"
    End If

    table.ConnectionProperties.DeleteAll

    table.ConnectionProperties.Add "Provider", P_currentConnection.Provider
    table.ConnectionProperties.Add "Data source", P_currentConnection.Properties("Data source").Value
    table.ConnectionProperties.Add "Database", P_currentConnection.DefaultDatabase
    table.ConnectionProperties.Add "Integrated security",  P_currentConnection.Properties("Integrated security").Value
    table.ConnectionProperties.Add "Persist Security Info", P_currentConnection.Properties("Persist Security Info").Value
    table.ConnectionProperties.Add "Initial Catalog", P_currentConnection.Properties("Initial Catalog").Value

    table.SetTableLocation table.location, "", P_currentConnection.ConnectionString

    table.TestConnectivity

Next table

It can be called with a procedure such as:
Dim crystal As CRAXDRT.Application, _
    m_report as CRAXDRT.report

Set crystal = New CRAXDRT.Application
Set m_rapport = crystal.OpenReport(nameOfTheReport & ".rpt")

connectreportToDatabase(m_report)

In case your report includes subreports, You might also have to redirect them to the active connection. In this case, you'll have to browse all objects in your report, check the ones that are of the report type and redirect them to the new connection. I am sure you'll have fun adding the corresponding extra lines to this original procedure.

A: You can get any of the info from the current report connection info. So if your not changing servers, then set the crystalServer variable to the reports current server.
'SET REPORT CONNECTION INFO
For i = 0 To rsource.ReportDocument.DataSourceConnections.Count - 1
    rsource.ReportDocument.DataSourceConnections(i).SetConnection(crystalServer, crystalDB, crystalUser, crystalPassword)
Next

For i = 0 To rsource.ReportDocument.Subreports.Count - 1
    For x = 0 To rsource.ReportDocument.Subreports(i).DataSourceConnections.Count - 1
        rsource.ReportDocument.OpenSubreport(rsource.ReportDocument.Subreports(i).Name).DataSourceConnections(x).SetConnection(crystalServer, crystalDB, crystalUser, crystalPassword)
    Next
Next

redpajama_set_name: RedPajamaStackExchange


text:
Q: Show/Hide fields on One2many tree - Odoo v8 I have some fields I'm showing in my One2many tree view:
  <page string="Budget Lines Planned">
            <field name="account_budget_bsi_line" colspan="4" nolabel="1" attrs="{'readonly':[('state','!=','draft')]}">
                <tree string="Budget Lines Planned" editable="bottom" >
                    <field name="opening_stock"/>
                    <field name="sales_planned" />
                    <field name="amount_total"/>
                    <field name="interauxiliary_transfers_planned" />
                    <field name="interauxiliary_receipts_planned" />
                    <field name="prod_purchased_planned" />
                    <field name="closing_stock_planned" />
                </tree>
            </field>
    </page>

This is from a custom module, which has a workflow with states, ie: draft, approved, next, done etc.
Suppose on next state, I want to hide opening_stock field, and show some other field.
I know this can be achieved on forms by using attrs="{'readonly':[('state','!=','draft')]}" or invisible or whatever.
But doesn't seem to work on One2many tree views, so, how can I achieve that in this case?

A: I'm fairly sure there is no way to dynamically hide an entire column of a One2many field's tree. You can dynamically hide the column's contents per row with attrs. In the case below, if the line had a Name of "Example", then it would show as a blank cell when in a Draft state.
<field name="opening_stock" attrs="{'invisible': [('state', '!=', 'draft')]}"/>

If you really must show a different One2many tree view, then you can try using multiple field/tree definitions in the view and using the attrs on the One2many field itself like so:
<field name="account_budget_bsi_line" attrs="{'invisible': [('state', '=', 'draft')]}">
    <tree>
        ...
        <field name="opening_stock"/>
        ...
    </tree>
</field>
<field name="account_budget_bsi_line" attrs="{'invisible': [('state', '!=', 'draft')]}">
    <tree>
        ...
        <!-- Exclude field opening_stock -->
        ...
    </tree>
</field>

I'm not sure if this will work for your needs, but it's the closest I can think to a solution.